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<?php
add_filter('body_class','add_category_to_single');
function add_category_to_single($classes, $class) {
  if (is_single() ) {
    global $post;
    foreach((get_the_category($post->ID)) as $category) {
      // add category slug to the $classes array
      $classes[] = $category->category_nicename;
    }
  }
  // return the $classes array
  return $classes;
}